Finance 371M, Money and Capital Markets, Fall 2015
Problem Set #5,
due Monday, 11/16/15 at 8:05am
I. Multiple Choice
(15 points total)
1. Of the sources of external funds for nonfinancial businesses in the United States, loans from
banks and other financial intermediaries account for approximately
of the total.
A) 6%.
B) 40%.
C) 56%.
D) 80%.
2. Of the following sources of funds for American nonfinancial businesses, the most important is
A) loans from banks.
B) retained earnings.
C) bonds and commercial paper.
D) loans from other financial intermediaries.
3. Of the following sources of external finance for American nonfinancial businesses, the least
important is
A) loans from banks.
B) stocks.
C) bonds and commercial paper.
D) loans from other financial intermediaries.
4. According to the Modigliani-Miller theorem,
A) a higher share of equity finance is better since it leads to a higher return on equity.
B) the way a firm raises funds does not matter for firm value under any circumstances.
C) the way a firm raises funds can matter for firm value if it affects the future cash flows of
the firm.
D) there are frequent arbitrage opportunities in the stock market.
5. If the value of an all equity-financed firm is 700, then the value of a firm with identical assets
that has perpetual and risk-free debt of 200 is
A) 900.
B) 760 if the interest rate on the debt is 5% and the corporate tax rate 30%.
C) 703 if the interest rate on the debt is 5% and the corporate tax rate 30%.
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D) also 700 due to the Modigliani-Miller theorem.
6. A firm wants to borrow $40 to fund a project that pays off $70 with prob. 0.6, and $30 with
prob. 0.4. If lenders require an expected return of 12%, the face value of the debt
A) is $54.67.
B) is $74.67.
C) is $40.
D) cannot be determined, since the project is too risky.
7. Debt overhang may cause equity holders of a firm to forgo a positive NPV project because
A) the interest rate on the firm’s existing debt is too high.
B) debt holders will block the project.
C) equity holders are too risk averse.
D) senior debt holders would capture a too large fraction of the project’s payoff.
8. Asset substitution by equity holders can be avoided if the fraction of debt financing is low
enough such that debt is
and the market value of debt is equal to
.
A) more profitable for lenders; that of equity
B) risk-free; its face value
C) riskier; the value of the project
D) senior; that of the whole firm.
in financial markets leads to adverse selection and moral hazard prob9. The presence of
lems that interfere with the efficient functioning of financial markets.
A) noncollateralized risk
B) free-riding
C) asymmetric information
D) costly state verification
10. The problem created by asymmetric information before the transaction occurs is called
while the problem created after the transaction occurs is called
.
,
A) adverse selection; moral hazard
B) moral hazard; adverse selection
C) costly state verification; free-riding
D) free-riding; costly state verification
11. The problem of adverse selection helps to explain
A) why firms are more likely to obtain funds from banks and other financial intermediaries,
rather than from securities markets.
B) why collateral is an important feature of consumer, but not business, debt contracts.
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C) why direct finance is more important than indirect finance as a source of business finance.
D) why lenders refuse loans to individuals with high net worth.
12. Since they require less monitoring of firms,
contracts to raise capital.
contracts are used more frequently than
A) debt; equity
B) equity; debt
C) debt; loan
D) equity; stock
13. Although debt contracts require less monitoring than equity contracts, debt contracts are still
subject to
since borrowers have an incentive to take on more risk than the lender would
like.
A) moral hazard
B) agency theory
C) diversification
D) the ”lemons” problem
14. On average, the stock price of a firm
such as
.
when a firm announces a leverage
event,
A) increases; decreasing; issuance of equity
B) decreases; decreasing; stock repurchases
C) increases; increasing; issuance of equity
D) increases; increasing; stock repurchases
15. If firms also have access to other forms of financing in an environment with asymmetric
information, the voluntary act of selling equity signals to investors that
A) debt financing is prohibitively expensive.
B) equity is likely to be overvalued.
C) equity is likely to be undervalued.
D) manager of the firm have less information than investors.
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II. Quantitative Problems
(30 points total)
1. (a) (4 points) Firm X’s business is not faring too well and the firm is expecting the following
cash flows next year:
– $90 with probability 0.1
– $0 with probability 0.9.
If the firm was to declare bankruptcy, the liquidation value of its assets would be equal
to $10. The firm has senior debt with face value of $50 on its books. The firm considers
a maintenance project that will cost $1 today and add $2 to its liquidation value.
(i) If the firm undertakes the maintenance project and is terminated due to bankruptcy
next year, what are the total cash flows in each scenario?
(ii) In order to fund the maintenance project, the firm needs to issue junior debt for $1.
What would the face value of the debt have to be?
(iii) Given the required face value from (ii), will the equity holders decide to issue the
junior debt and invest? How does their decision affect the value of the senior debt?
(b) (4 points) Firm Y can choose between two projects. Project S pays $60 for certain.
Project R pays
– $100 with probability 0.5
– $10 with probability 0.5.
Both projects require initial outlays of $50.
(i)
(ii)
(iii)
(iv)
Compute the expectation and the standard deviation of the NPV for each project.
If debt is used to finance project, what is the required face value, F, of the bond?
Which project will equity holders choose?
What is the maximum amount of the debt (face value) the firm can take on such
that equity owners will optimally choose the safe project?
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2. (10 points) Suppose there is a large population of firms with two types, H and L. Each firm
has some assets in place, and access to an investment project. The value of the assets in place
is given by Ai , for i = H and L, respectively. The payoff of the investment project is the same
for both types of firms and given by R. To execute the project, an initial investment of I is
required, with R > I > 0. The fraction of type-H firms is q.
Further assume firms do not have any cash and the only way to obtain funds is to sell a share
of the company. Investors in the equity market do not know the type of the firm at the time
of investment, are risk-neutral, and require an expected return of at least zero.
(a) State the general condition under which H-type firms issue equity and execute the project
in equilibrium. Intuitively, why may this condition fail?
(b) Assume AH = 85, AL = 45, R = 15, and I = 10. Find the lowest possible value of q
such that both types of firms issue and invest in equilibrium; that is, find q such that if
q > q, good firms issue equity and execute the project.
(c) Now assume that everything is as in part (b), but in addition firms have some cash on
hand C = 5, so that they only need to raise I − C = 5 units of capital by issuing equity.
What is the value of q now? Explain.
(d) Now assume that everything is as in part (b) and that q = 0.2. In addition, firms of
both types have access to debt funding. Specifically, they can get a loan with principal
amount 10 today and an interest rate of 10%. Do managers of H-type firms prefer debt
funding over equity issuance in this case? What about L-type firms? What does this
imply for the market valuation V ∗ of equity being issued?
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3. (12 points) An entrepreneur wants to fund a project that requires an investment of $10,000
and has the following payoffs next year:
40,000 with probability 0.8,
10,000 with probability 0.1,
and 0 with probability 0.1.
Only the entrepreneur can observe the true outcome of the project. Investors require a 10%
return.
(a) Suppose verifying the payoff is impossible so that liquidation that wipes out all of a
firm’s cash is the outcome in the event of default. What is the optimal face value of
debt? What are the expected lost revenues (“costs of financial distress”) due to default?
(b) Now suppose that the payoff can be verified for a cost of $2,500. What is the optimal
face value of debt now? What are the expected lost revenues due to default now?
(c) Assume the entrepreneur has $2,000 of his own cash, and monitoring is still possible
for $2,500 as in (b). If the entrepreneur invests all of the $2,000 into the project and
thus only needs to borrow $8,000, what is the optimal face value of debt? What are the
expected lost revenues due to default?
(d) How does your answer to (c) change if the entrepreneur has $2,100 in cash instead and
thus only needs to borrow $7,900? [Hint: Does the entrepreneur still need to declare
bankruptcy if the outcome is 10,000 now?]
(e) Assume again the entrepreneur has $2,000 as in (c), and that this money could alternatively be invested at 10% (safe return). Should the entrepreneur invest his own money
into the project as in part (c), or borrow the whole $10,000 (and invest the $2,000 at
10%)?
(f) What is the maximum amount the entrepreneur could borrow without putting up any
money of his own?
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